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In this article, the simultaneous fault detection and consensus control (SFDCC) problem of multiple Lur'e systems is investigated under unknown faults and external disturbances. First, a novel distributed consensus controller based on the distributed event-triggering mechanism and a novel distributed FD method based on the distributed event-triggered observer are developed. In order to design an appropriate consensus controller and a FD observer so that the associated residual signals are susceptible to unknown faults and are robust to external disturbances. A hybrid $ {{H_-}/{H_{\infty }}}$ method is used to transform the particular design problem into an optimization problem, and sufficient conditions are obtained to satisfy the optimization performance constraints. Then, a residual evaluation method is proposed based on a dynamic residual function threshold. The results show that under the proposed distributed event-triggered SFDCC method, consensus as well as FD of multiple Lur'e systems can be achieved simultaneously. The proposed method could be able to avoid continuous observation of neighboring agents' information, and thus, validly reduce the amount of communication. Moreover, the proposed method could achieve higher accuracy of FD than that based on the traditional static residual function threshold. Finally, the numerical simulation case is performed to demonstrate the availability of the proposed method.

This article considers the dynamic event-triggered simultaneous fault detection and leader-following consensus (SFDLFC) problem for nonlinear multiagent systems (MASs) with directed graphs. First, based on the distributed fault detection (FD) observer, a distributed dynamic event-triggered consensus controller is designed together with a dynamic event-triggering mechanism (DETM) to achieve leader-following consensus of MASs under directed graphs and lessen the amount of data transmission between neighboring agents. Then, a residual evaluation mechanism is developed under directed graphs to detect and isolate the faulty agent. To make the residual signal sensitive to the faults and robust to the tracking errors, a hybrid $H_{\infty }/H_{-}$ method is used to transform the design problem of consensus controller and FD observer into a multiobjective optimization problem, and sufficient conditions are obtained to satisfy the optimization performance constraints by Lyapunov theory. It should be noted that compared with the existing related works, our main contribution is that the proposed method could achieve consensus and detect faults of MASs under a more general communication graph, and the proposed DETM could generate larger triggering intervals and therefore achieve better resource efficiency. Finally, a simulation result is provided to demonstrate the effectiveness of the proposed technique.

δ-AlOOH has emerged as a promising candidate for water storage in the lower mantle and could have delivered water into the bottom of the mantle. To date, it still remains unclear how the presence of iron affects its elastic, rheological, vibrational, and transport properties, especially across the spin crossover. Here, we conducted high-pressure X‑ray emission spectroscopy experiments on a δ-(Al0.85Fe0.15) OOH sample up to 53 GPa using silicone oil as the pressure transmitting medium in a diamond-anvil cell. We also carried out laser Raman measurements on δ-(Al0.85Fe0.15)OOH and δ-(Al0.52Fe0.48)OOH up to 57 and 62 GPa, respectively, using neon as the pressure-transmitting medium. Evolution of Raman spectra of δ-(Al0.85Fe0.15)OOH with pressure shows two new bands at 226 and 632 cm−1at 6.0 GPa, in agreement with the transition from an ordered (P21nm) to a disordered hydrogen bonding structure (Pnnm) for δ-AlOOH. Similarly, the two new Raman bands at 155 and 539 cm−1appear in δ-(Al0.52Fe0.48)OOH between 8.5 and 15.8 GPa, indicating that the incorporation of 48 mol% FeOOH could postpone the order-disorder transition upon compression. On the other hand, the satellite peak (Kβ′) intensity of δ-(Al0.85Fe0.15)OOH starts to decrease at ~30 GPa and it disappears completely at 42 GPa. That is, δ-(Al0.85Fe0.15)OOH undergoes a gradual electronic spin-pairing transition at 30–42 GPa. Furthermore, the pressure dependence of Raman shifts of δ-(Al0.85Fe0.15)OOH discontinuously decreases at 32–37 GPa, suggesting that the improved hydrostaticity by the use of neon pressure medium could lead to a relatively narrow spin crossover. Notably, the pressure dependence of Raman shifts and optical color of δ-(Al0.52Fe0.48)OOH dramatically change at 41–45 GPa, suggesting that it probably undergoes a relatively sharp spin transition in the neon pressure medium. Together with literature data on the solid solutions between δ-AlOOH and ε-FeOOH, we found that the onset pressure of the spin transition in δ-(Al,Fe)OOH increases with increasing FeOOH content. These results shed new insights into the effects of iron on the structural evolution and vibrational properties of δ-AlOOH. The presence of FeOOH in δ-AlOOH can substantially influence its high-pressure behavior and stability at the deep mantle conditions and play an important role in the deep-water cycle.